If in the year 2021, the expenditure of Company A was equal to the expenditure…
2024
If in the year 2021, the expenditure of Company A was equal to the expenditure of Company B, then what was the ratio of their respective incomes?
Answer: B. 32:29 — Concept: Profit percentage is calculated on expenditure: Profit % = (Income − Expenditure) / Expenditure × 100. Therefore, Income = Expenditure × (1 + Profit…
- A.
3:2
- B.
32:29
- C.
2:5
- D.
7:5
Show answer & explanation
Correct answer: B
Concept: Profit percentage is calculated on expenditure: Profit % = (Income − Expenditure) / Expenditure × 100. Therefore, Income = Expenditure × (1 + Profit % / 100).
When two companies have equal expenditure, their income ratio is (100 + first profit rate) : (100 + second profit rate).
Application
Let the equal expenditure of each company be E.
In 2021, Company A earned 60% profit and Company B earned 45% profit.
Company A income = E × (1 + 60/100) = E × (1 + 0.60) = E × 1.60 = 1.60E.
Company B income = E × (1 + 45/100) = E × (1 + 0.45) = E × 1.45 = 1.45E.
Therefore, A:B = 1.60E:1.45E. Cancelling the common factor E gives 1.60:1.45.
Multiplying both terms by 100 gives 160:145; dividing both by their common factor 5 gives 32:29.
Cross-check
Taking E = 100 gives incomes 160 and 145. Their ratio is 160:145, which reduces to 32:29.
Result: The required income ratio is 32:29.